Higher Order Derivatives
Published in
2 min readJan 23, 2019
- First order derivative:
f'(x)
ordy/dx
, also called "First Derivative" - Second order derivative:
f''(x)
ord²y/dx²
, also called "Second Derivative" - …
Second derivatives
The second derivative of a function is simply the derivative of the function’s derivative.
Notation:
Leibniz’s notation for second derivative is:
Second derivatives of implicit equations
▶ Back to previous note on Implicit Differentiation
▶ Practice at Khan academy: Second derivatives (implicit equations)
▶ Online calculator for 2nd Derivative of Implicit equations
Example
Solve:
Example
Solve:
- The first derivative is:
- The second derivative is:
- Plug in
y=1
, and get: